半群的Ω-模糊子半群

Ω-Fuzzy Subsemigroup of Semigroups

给定一个集合Ω,引入半群的Ω-模糊子半群的概念,研究其一些基本性质。给出半群的Ω-模糊子半群的等价刻画,证明了半群的Ω-模糊子半群的交、同态像与原像等也是半群的Ω-模糊子半群。最后,通过在SΩ上定义运算得到半群(SΩ,),并研究了其模糊子半群与Ω-模糊子半群。

Given a set Ω,the Ω-fuzzy subsemigroup of the semigroup is introduced,and the basic propeities are investigated. Several equivalent characterizations of the Ω-fuzzy subsemigroup are obtained. We prove that the intersection of two Ω-fuzzy subsemigroups,the homomorphism image or homomorphism preimage of the Ω-fuzzy subsemigroup are the Ω-fuzzy subsemigroup. By defining the multiply operation in Sa we obtain the semigroup （S^Ω, ）, investigate its fuzzy subsemigroup and Ω-fuzzy subsemigroup.